Cosmology Dark Energy Models ASTR 2120 Sarazin

Transcription

1 Cosmology Dark Energy Models ASTR 2120 Sarazin

2 Late Homeworks Last day Wednesday, May 1 My mail box in ASTR 204 Maximum credit 50% unless excused (but, better than nothing)

3 Final Exam Thursday, May 2, 9:00 am - noon ASTR 265 (classroom) You may not consult the text, your notes, or any other materials or any person You can bring three 3x5 index cards with equations only on both sides! Bring pencils, paper, calculator

4 Final Exam ~2/3 Quantitative Problems (like homework problems) ~1/3 Qualitative Questions Multiple Choice (scantron), Short Answer, Fill In the Blank No essay questions Scantron = need pencils and eraser

5 Final Exam (Cont.) Material: Final exam will cover the entire semester Chapters (5), 7, Stars, Sun Cosmology Extra emphasis on material not on first two tests Clusters of Galaxies (problems), AGNs, Cosmology Chapters 21, 23, 24 Homeworks 9-11 Know pc, AU, M solar, L solar, R solar, H 0, T CMB

6 Final Exam (Cont.) Review Session: Wednesday, May 1(Reading Day) 10 am - noon ASTR 265 (classroom) Mainly material since test 2?

7 Cosmology Dark Energy Models ASTR 2120 Sarazin

8 Cosmological Constant Model History: Einstein (~1917) realizes there are no static cosmological models in General Relativity Obvious: gravity is only force in models, always attractive, nothing to balance gravity Einstein says: Universe is obviously static something is wrong Einstein adds a fudge Cosmological Constant = L = gravity (actually, anti-gravity) without matter Empty Universe would expand, add matter and gravity (exactly the right amount) gravity = - Cosmological Constant Static universe (but unstable)

9 Cosmological Constant Model History (cont): Hubble expansion (1920 s) Universe is expanding, not static Had Einstein been brave enough, would have predicted Hubble expansion The biggest mistake of my life - Einstein

10 Cosmological Constant Model Subsequent History: Quantum Mechanics vacuum fluctuations vacuum energy Uncertainty Principle: ΔE Δt E(vacuum) 0 + ΔE = 0 + 2m e c 2 for example for short time, Δt /(2m e c 2 ) Make e e + pair, then disappear

11 Cosmological Constant Model e + e - e + e+ e + e - e - e - e - e + Vacuum = bubbling sea of particles and antiparticles effective pressure of virtual particles repulsive force in vacuum Could L be real?

12 Cosmological Constant Model Subsequent History: Distances from SN Ia expansion of Universe is accelerating Standard Models are wrong Dark Energy

13 Cosmological Constant Model Λ has units of 1/(distance) 2 Note : Λ (text) = Λ(here) c 2 Λ 3 (curvature of vacuum) Equivalent to : mass density : ρ Λ = Λc2 8πG Ω Λ ρ Λ = 1 Λc 2 2 ρ crit 3 H 0 vacuum energy density : u Λ = ρ Λ c 2 pressure : P Λ = ρ Λ c 2 = u Λ NEGATIVE!!

14 Cosmological Constant Model Negative Pressure?! Vacuum energy density = u L = r L c 2 Consider vacuum created when Universe expands: P L V DV New energy created DE = u L DV, energy conserved, must come from somewhere Work done by vacuum (fluctuation gas ): W = P L DV = - DE = - u L DV P L = - u L negative pressure Old Dark Energy creates new Dark Energy

15 Cosmological Constant Model Like Newtonian potential energy : Φ Λ = 1 6 Λc2 r 2 F acceleration : a = Φ Λ = Λc2 r r radial repulsive force d(r /r o ) dt Ω = H M o (r /r o ) + Kc2 2 H 0 + Λc2 3H 0 2 ' ) ( r r o *, + 2 d(r /r o ) dt Ω = H M o (r /r o ) + Kc2 2 H 0 + Ω ' r Λ) ( r o *, + 2 Equation of Cosmic Dynamics Friedmann Equation

16 Cosmological Constant Model d(r /r o ) dt Curvature : K = H 2 0 c 2 = H o Ω M (r /r o ) + Kc2 H Ω Λ ( Ω M + Ω Λ 1) Dark Energy and Matter have same effect on curvature Deceleration parameter : $ & % r r o ' ) ( 2 q o = 1 2 Ω M Ω Λ Dark Energy = accelerated expansion Dark Energy and Matter have opposite effect on dynamics

17 Cosmological Constant Model d(r /r o ) dt = H o Ω M (r /r o ) + Kc2 H Ω Λ Ω M Mass term r 1/2 dominates early Ω Λ Dark Energy term r dominates late $ & % r r o ' ) ( 2 r / r o t o acceleration deceleration t

18 Cosmological Constant Model Late times: r / r 0 >>1 (r / r o ) = Aexp( H o Ω Λ t) exponential expansion!!

19 What is Dark Energy? Problem with Dark Energy: If you actually try to calculate the effect of vacuum fluctuations on gravity they are either: ~ x too large!!! or 0 or ~ x too small!!! depending on assumptions No current theory gives the correct value!!

20 Cosmology - Tests ASTR 2120 Sarazin WMAP Satellite

21 Cosmological Tests What is K? W M? Is there a Cosmological Constant? Local Tests: Measurement in local (low redshift) Universe 1. Hubble Constant (discussed earlier) 2. Age limit from oldest stars (homework) or radioactivity 3. Current average density Measure <r> W M = r / r crit

22 Local Cosmological Tests Clusters of Galaxies Big enough to be fair sample of Universe Measure total mass, baryon mass Scale to whole Universe W M = 0.3 Low density Universe

23 Global Cosmological Tests Measure objects at high redshift to determine 1. Change in expansion with redshift (time) 2. Geometry of Universe 1920 s - late 1990 s: Mainly done with galaxies, assuming they are standard candles Effect small, data bad, galaxies evolve

24 Type Ia Supernovae Reminder: believed to be due to white dwarf in binary accreting to over the Chandrasekhar limit " M Ch = 0.78 c % $ ' # G & 3/2 1 m p 2 =1.4M Best defined objects in astrophysics? However, nature of binary companion and details of the explosion are uncertain

25 Type Ia Supernovae All have similar peak luminosities Variation correlates with decay time for light Benefits: 1. Very bright, can be seen across Universe 2. Occur among old stars. Look in elliptical galaxies, no young stars, no core-collapse SN 3. Ellipticals = little gas or dust, little extinction

26 Type Ia Supernovae

27 Type Ia Supernovae

28 Type Ia Supernovae

29 Type Ia Supernovae Supernovae at high redshift fainter than expected for velocity, or equivalently slower for distance Expansion of Universe is accelerating with time! W L > 0.3 just from SN Ia

30 CMB Fluctuations and WMAP CMB photons come directly to us from t = 370,000 years after Big Bang when temperature was 3000 K Fluctuations in density of matter and radiation (later become galaxies, etc.) First seen with COBE satellite

31 CMB Fluctuations and WMAP Fluctuations on all scales, but... Acoustic peak at l = (sound speed) x age Know age (370,000 years) and sound speed (T = 3000 K) know l (actually full spectrum)

32 CMB Fluctuations and WMAP

33 CMB Fluctuations and WMAP Fluctuations on all scales, but... Acoustic peak at l = (sound speed) x age Know age (370,000 years) and sound speed (T = 3000 K) know l (actually full spectrum) Known size objects at known distance and redshift = angular size determines geometry

34 CMB Fluctuations and WMAP

35 CMB Fluctuations and WMAP

36 WMAP Satellite

37 WMAP Fluctuations

38 WMAP Fluctuations

39 WMAP Fluctuations Flat Universe WM + WL = 1

40 Concordance Cosmology WMAP & Planck CMB Fluctuations: Flat Universe SN Ia: W M + W L» 1 Accelerated expansion Clusters: Low density Universe W M» 0.3

41 WMAP 9 Year Cosmology H 0 = 71 km/sec/mpc (from other measurements) W M = 0.29 W L = % Dark Energy, 24% Dark Matter, 5% Baryons Flat Universe W M + W L» 1 Accelerating Universe, will expand forever (?) Age of Universe t 0 = 13.8 billion years

42 Concordance Cosmology

43 Concordance Cosmology

44 Cosmology - Redshift and Radiation ASTR 2120 Sarazin

45 Redshift in Cosmology z º (l obs - l em )/l em 0 z < 1 + z = l obs / l em Straightforward to measure Astronomer prefer to Distance from us Model dependent 0 < d < d H (size of observable Universe), all of early Universe compressed near d = d H ) Age or time into past (compressed near t 0 ) Model dependent

46 Redshift in Cosmology Interpretation of Redshift z? Low redshifts, z << 1, nearby Universe: Straightforward: redshift is Doppler shift z º (l obs - l em )/l em» v r /c» H 0 d (v r << c) High redshifts, z 1, distant Universe and past time: Hubble formula breaks down Relativistic Doppler shift? Effect of change in expansion rate of Universe, H(t)? Gravitational redshift? Effects of curvature of photon paths?

47 Redshift in Cosmology Sounds difficult to calculate, confusing, and very model dependent a big pain?? Then, a miracle occurs... Oh no, my head is going to explode!!

48 Redshift in Cosmology Divide photon path into lots of very small pieces, treat each as series of emissions and observations For each piece, time dt << t H, length dl << d H Just like low redshifts, dz << 1, nearby Universe: Straightforward: redshift is first order Doppler shift Relativistic Doppler shift? Effect of change in expansion rate of Universe, H(t)? Gravitational redshift? Effects of curvature of photon paths?

49 Redshift in Cosmology dl = cdt distance traveled by photon dv = H(t)dl = H (t)cdt Hubble expansion law H(t)= 1 r dv = c 1 r dr dt dr dt r = radius of Universe dt = c dr r << c z = λ obs λ em λ em redshift dz = dλ λ <<1 where dλ = λ obs λ em, and λ obs λ em dz = dλ λ = dv c = 1 c c dr r = dr r

50 Redshift in Cosmology dλ λ = dr integrate both sides r dλ dr = λ r lnλ = ln r + constant lnλ = ln r + lnλ em lnr em % ln λ ( % ' * = ln r ( ' * & ) & ) λ em r em λ obs λ em = r obs r em

51 Redshift in Cosmology λ obs λ em = r obs r em z = λ obs λ em λ em = λ obs λ em 1 1+ z = r obs r em Big Bang : r em 0 z Wavelengths just expand with Universe!! Really, it could not have turned out to be simpler or nicer!

52 Redshift in Cosmology

53 Redshift in Cosmology λ obs λ em = r obs r em z = λ obs λ em λ em = λ obs λ em 1 1+ z = r obs r em Big Bang : r em 0 z Wavelengths just expand with Universe!! Really, it could not have turned out to be simpler or nicer!

54 Redshift in Cosmology Example: Recently, there was a claim that the Hubble Ultra Deep Field contains a galaxy with a redshift of z = 10 When this galaxy emitted the light we now see, the Universe was (1+z) = 11 times smaller than it is today!!

55 Cosmic Microwave Background (CMB) T = K Awfully cold - who cares? a) Most of known heat and free energy in Universe b) Most of photons in Universe N(photons)/N(protons) ~ 10 9 (Homework problem) Where did this big number come from? Why isn t it bigger? If matter and antimatter were symmetric p + p 2γ N(photons)/N(protons) Bright and shiny (but empty) Universe!!

56 Cosmic Microwave Background VERY hot in the past: (CMB) Theorem: Redshifted and expanded blackbody = blackbody at redshifted temperature (homework) λ T γ = constant (T γ CMB temperature) T γ ( z) = ( 1+ z)t γo

57 Cosmic Microwave Background Example: (CMB) Recently, there was a claim that the Hubble Ultra Deep Field contains a galaxy with a redshift of z = 10 When this galaxy emitted the light we now see, the CMB temperature was (1+z) = 11 times larger than it is today = 30 K

58 CMB at z=10 Galaxy Belliac Labs 30 K Pensiac Wilsoniac

59 Cosmic Microwave Background (CMB) λ T γ = constant (T γ CMB temperature) T γ ( z) = ( 1+ z)t γo (1 + z) = r o / r e as Big Bang is approached, so T at Big Bang

60 Hot Big Bang